Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The gas in A is compressed isothermally to 1/8 of its original volume while the gas in B is compressed adiabatically to 1/8 of its original volume. The ratio of final pressure of gas in B to that of gas in A is

Solution

Physics sir · 3 steps

Find each final pressure on its own, then divide: 8^(5/3) over 8 leaves 8^(2/3) = 4.

1. Isothermal gas A. At constant temperature PV stays fixed. The volume becomes V/8, so the pressure becomes P_A = 8P.
2. Adiabatic gas B. For an adiabatic process PV^γ stays fixed, and a monoatomic gas has γ = 5/3. So P_B = P × 8^(5/3) = P × 2⁵ = 32P.

   P_B/P_A = 8^γP/8P = 8^(γ - 1) = 8^(2/3) = 4

3. So. The adiabatic gas ends at 4 times the pressure of the isothermal gas, which is option (c).

The idea to keep. Compress by a factor r: isothermal multiplies P by r, adiabatic by r^γ. Their ratio is r^(γ-1), and for a monoatomic gas γ = 5/3.

Answer from the NTA final answer key. Solution by PrepWiser.